A Lagrangian discretization multiagent approach for large-scale multimodal dynamic assignment

This paper develops a Lagrangian discretization multiagent model for large-scale multimodal simulation and assignment. For road traffic flow modeling, we describe the dynamics of vehicle packets based on a macroscopic model on the basis of a Lagrangian discretization. The metro/tram/train systems are modeled on constant speed on scheduled timetable/frequency over lines of operations. Congestion is modeled as waiting time at stations plus induced discomfort when the capacity of vehicle is achieved. For the bus system, it is modeled similar to cars with different speed settings, either competing for road capacity resources with other vehicles or moving on separated bus lines on the road network. For solving the large-scale multimodal dynamic traffic assignment problem, an effective-path-based cross entropy is proposed to approximate the dynamic user equilibrium. Some numerical simulations have been conducted to demonstrate its ability to describe traffic dynamics on road network.multimodal transportation systems; Lagrangian discretization; traffic assignment; multiagent systems

a cross-entropy based multiagent approach for multiclass activity chain modeling and simulation

This paper attempts to model complex destination-chain, departure time and route choices based on activity plan implementation and proposes an arc-based cross entropy method for solving approximately the dynamic user equilibrium in multiagent-based multiclass network context. A multiagent-based dynamic activity chain model is developed, combining travelers' day-to-day learning process in the presence of both traffic flow and activity supply dynamics. The learning process towards user equilibrium in multiagent systems is based on the framework of Bellman's principle of optimality, and iteratively solved by the cross entropy method. A numerical example is implemented to illustrate the performance of the proposed method on a multiclass queuing network.dynamic traffic assignment, cross entropy method, activity chain, multiagent, Bellman equation

A kinematic wave theory of capacity drop

Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a simple model of capacity drop within the framework of kinematic wave theory based on the observation that capacity drop occurs when an upstream queue forms at an active bottleneck. In addition, we assume that the fundamental diagrams are continuous in steady states. This assumption is consistent with observations and can avoid unrealistic infinite characteristic wave speeds in discontinuous fundamental diagrams. A core component of the new model is an entropy condition defined by a discontinuous boundary flux function. For a lane-drop area, we demonstrate that the model is well-defined, and its Riemann problem can be uniquely solved. We theoretically discuss traffic stability with this model subject to perturbations in density, upstream demand, and downstream supply. We clarify that discontinuous flow-density relations, or so-called "discontinuous" fundamental diagrams, are caused by incomplete observations of traffic states. Theoretical results are consistent with observations in the literature and are verified by numerical simulations and empirical observations. We finally discuss potential applications and future studies.Comment: 29 pages, 10 figure

Generalised Mertens and Brauer-Siegel Theorems

In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to make it tend to infinity and thus to point out the link between it and the famous Brauer-Siegel theorem. Using this we deduce an explicit version of the generalised Brauer-Siegel theorem under GRH, and a unified proof of this theorem for asymptotically exact families of almost normal number fields

On the Number of Rational Points of Jacobians over Finite Fields

In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta-functions